Question

A person hums in a well and finds strong resonance at frequencies $60$Hz, $100$Hz and $140$Hz. What is the fundamental frequency of the well? Explain? How deep is the well?(velocity of sound $=344$ m/s).

Answer 1

resonating frequencies $\to 60Hz,100Hz,140Hz$

spend of sound $=344m/s$

Well behaves as organ pipe with are end closed

only odd harmonics are allowed

$(2n-1)\frac{\lambda }{4}=l\Rightarrow \frac{(2n-1)V}{4f}=l$

$(2m-1)\frac{344}{4\times 60}=(2n-1)\frac{344}{4\times 100}=(2p-1)\frac{344}{4\times 100}$

$\frac{2m-1}{6}=\frac{2n-1}{10}=\frac{2p-1}{14}=A$

The fundamental frequency is $20Hz$ because $60Hz$ corresponds to $3^{rd}$ harmonic

$l=(2n-1)\frac{V}{2f}=\frac{1\times 344}{4\times 20}=4.3m$